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Finite-spectral recovery of Weyl-blind twisting modes

Scott Schubr

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Abstract

Odd logarithmic twisting modes in a fixed polar-strip tube are invisible to the leading Weyl profile but detectable in the next heat profile. We give a quantitative continuation of this complete-spectrum result. An estimate on the actual curved normal cap yields heat remainder O(T^(17/6)), and hence normalized bias O(T^(-1/6)). A complete finite spectral prefix, certified spectral uncertainties, a counting envelope and a certified complex multiplier enclosure then give a deterministic recovery disk. With exact spectral inputs its fixed-mode cutoff rate is O((logΛ/Λ)^(1/12)); the relative-noise balance is O(σ^(1/7)) before inversion of the heat multiplier. A long-straight-core construction proves why a uniform geometric prior is necessary. Two-sided multiplier bounds quantify exponential conditioning of the ideal lower heat profile. The geometric remainder constants exist but are not fully evaluated numerically. A concrete fundamental-mode interval execution is valid and noninformative.

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Edition files

Available editions

  1. Edition 2 · 2026-10-27 · public
  2. Edition 1 · 2026-10-23 · public

Research details

Subjects
Mathematics · Analysis and Spectral Theory
Keywords
inverse spectrum, twisted tubes, finite spectral data, deterministic error bounds, geometric priors
Manuscript date
2026-10-23
Reader reuse
No additional permission granted

Scope

Certified finite-spectral recovery disks and sufficient cutoff/noise rates for fixed Weyl-blind twist modes under controlled geometry, with multiplier conditioning and a necessary geometric prior.

Disclosures

Author-posted preprint. AI-assisted internal research and verification do not constitute external human peer review or proof-assistant formalization.

Reproduction

10-page manuscript and 11 source-package members. Compile main.tex; the two included nine-page predecessor PDFs supply the cited heat expansion and all-odd noncancellation dependencies. Standard-library check_conditioning.py checks exact scalar bounds. With Python 3.12 and python-flint 0.9.0, run concrete_spectral.py in a writable extracted copy, then concrete_recovery.py --output recovery.json to reproduce the valid noninformative interval example and unchanged prior.

References and related resources

  1. S. Schubr, Heat-Trace Recovery of a Weyl-Blind Twisting Mode , edition 1 (2026), companion manuscript supplied with this paper.
  2. S. Schubr, Audibility of all odd blind modes in rapidly twisted polar-strip tubes , edition 1 (2026), companion manuscript supplied with this paper.
  3. D. Krejčiřík, Waveguides with asymptotically diverging twisting , Applied Mathematics Letters 46 (2015), 7–10. arXiv:1407.4028.
  4. T. Coulhon and A. Sikora, Gaussian heat kernel upper bounds via the Phragmén–Lindelöf theorem , Proceedings of the London Mathematical Society (3) 96 (2008), 507–544. arXiv:math/0609429.
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